
Lagrange Multipliers
(Don't worry, this isn't the same question as I posted the other day)
Find the maximum value of
subject to the constraint
[NB: your answer should be given as a surd, not a decimal.]
To begin with, I multiplied out the function to get
Is that right? If not, can you tell me why? If it is, I then got the following partials...
...but then rearranging for , , , and put them into I get a really awful expression for and consequently awful expressions for , and (not 'cause I get that equal to ) (Worried)
Can anyone maybe see where I've gone wrong? I can tell you what I got for et cetera if needs be.

If the going gets rough when doing a math exercise, it's always worth checking whether you copied the question correctly. I'm wondering whether those fourth powers should really be squares. That would make things a lot less unpleasant.
Assuming that they really are fourth powers, you just have to roll up your sleeves and persevere with the calculations. Your partial derivative equations tell you that , and . Then the equation becomes , from which . Then , and x and y are the same expression multiplied by .
So it's all a bit messy, but not impossibly hard.